Students were asked to prove the identity (sec x)(csc x) =

Last updated: 8/13/2022

Students were asked to prove the identity (sec x)(csc x) = cot x + tan x. Two students' work is given. Student A Step 1: Step 2: cos X sin x Step 5: 1 cos x sin x Step 4: cos²x Step 3: cosx+sin² cos x sin x cos x sinx COS X sinx 11: = cot x + tan x cotx + tan x X cot x + tan x sin² x cos x sin x sin x COS X 11 cotx + tan x Student B Step 6: cot x + tan x = cot x + tan x Step 1: secxcsc x = Step 2: secxcscx = cotx + tanx Step 4: secxcscx = Step 3: secxcsc x = cos x sin x Step 5: secxcsc x = sinx cos x cos²x cosxsin x cos²x+sin² x cos x sin x 1 cos x sinx sin² x cos xsin x (x)(sinx) Step 6: sec x csc X = sec x csc X Part A: Did either student verify the identity properly? Explain why or why not. (10 points) Part B: Name two identities that were used in Student A's verification and the steps they appear in. (5 poin